Irreducible inclusions of simple C*-algebras

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Standard

Irreducible inclusions of simple C*-algebras. / Rørdam, Mikael.

In: L’Enseignement Mathématique, Vol. 69, No. 3, 2023, p. 275-314.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Rørdam, M 2023, 'Irreducible inclusions of simple C*-algebras', L’Enseignement Mathématique, vol. 69, no. 3, pp. 275-314. https://doi.org/10.4171/LEM/1051

APA

Rørdam, M. (2023). Irreducible inclusions of simple C*-algebras. L’Enseignement Mathématique, 69(3), 275-314. https://doi.org/10.4171/LEM/1051

Vancouver

Rørdam M. Irreducible inclusions of simple C*-algebras. L’Enseignement Mathématique. 2023;69(3):275-314. https://doi.org/10.4171/LEM/1051

Author

Rørdam, Mikael. / Irreducible inclusions of simple C*-algebras. In: L’Enseignement Mathématique. 2023 ; Vol. 69, No. 3. pp. 275-314.

Bibtex

@article{c84e514f11934f3cb4c1ed4a453b5105,
title = "Irreducible inclusions of simple C*-algebras",
abstract = "The literature contains interesting examples of inclusions of simple C ∗ -algebras with the property that all intermediate C ∗ -algebras likewise are simple. In this article we take up a systematic study of such inclusions, which we refer to as being C ∗ -irreducible by the analogy that all intermediate von Neumann algebras of an inclusion of factors are again factors precisely when the given inclusion is irreducible.We give an intrinsic characterization of when an inclusion of C ∗ -algebras is C ∗ -irreducible, and use this to revisit known and exhibit new C ∗ -irreducible inclusions arising from groups and dynamical systems. Using a theorem of Popa one can show that an inclusion of II1-factors is C ∗ -irreducible if and only if it is irreducible with finite Jones index. We further show how one can construct C ∗ -irreducible inclusions from inductive limits, and we discuss how the notion of C ∗ -irreducibility behaves under tensor products.",
author = "Mikael R{\o}rdam",
year = "2023",
doi = "10.4171/LEM/1051",
language = "English",
volume = "69",
pages = "275--314",
journal = "Enseignement Mathematique",
issn = "0013-8584",
publisher = "European Mathematical Society Publishing House",
number = "3",

}

RIS

TY - JOUR

T1 - Irreducible inclusions of simple C*-algebras

AU - Rørdam, Mikael

PY - 2023

Y1 - 2023

N2 - The literature contains interesting examples of inclusions of simple C ∗ -algebras with the property that all intermediate C ∗ -algebras likewise are simple. In this article we take up a systematic study of such inclusions, which we refer to as being C ∗ -irreducible by the analogy that all intermediate von Neumann algebras of an inclusion of factors are again factors precisely when the given inclusion is irreducible.We give an intrinsic characterization of when an inclusion of C ∗ -algebras is C ∗ -irreducible, and use this to revisit known and exhibit new C ∗ -irreducible inclusions arising from groups and dynamical systems. Using a theorem of Popa one can show that an inclusion of II1-factors is C ∗ -irreducible if and only if it is irreducible with finite Jones index. We further show how one can construct C ∗ -irreducible inclusions from inductive limits, and we discuss how the notion of C ∗ -irreducibility behaves under tensor products.

AB - The literature contains interesting examples of inclusions of simple C ∗ -algebras with the property that all intermediate C ∗ -algebras likewise are simple. In this article we take up a systematic study of such inclusions, which we refer to as being C ∗ -irreducible by the analogy that all intermediate von Neumann algebras of an inclusion of factors are again factors precisely when the given inclusion is irreducible.We give an intrinsic characterization of when an inclusion of C ∗ -algebras is C ∗ -irreducible, and use this to revisit known and exhibit new C ∗ -irreducible inclusions arising from groups and dynamical systems. Using a theorem of Popa one can show that an inclusion of II1-factors is C ∗ -irreducible if and only if it is irreducible with finite Jones index. We further show how one can construct C ∗ -irreducible inclusions from inductive limits, and we discuss how the notion of C ∗ -irreducibility behaves under tensor products.

U2 - 10.4171/LEM/1051

DO - 10.4171/LEM/1051

M3 - Journal article

VL - 69

SP - 275

EP - 314

JO - Enseignement Mathematique

JF - Enseignement Mathematique

SN - 0013-8584

IS - 3

ER -

ID: 382503553